PrefaceThe modeling of forest ecosystems is one of IIASA's continuous research activities in the Environment Program. There are two main approaches to this modeling: (a) simulation, and (b) qualitative (analytical) . This paper belongs to the latter.Analytical models allow the prediction of the behavior of key variables of ecosystems and can be used to organize and analyze data produced by simulation models or obtained by observations. This paper is devoted to the study of a simple mathematical model of spatially distributed noneven-age forests. The main tools used in the paper are new methods of qualitative theory of non-linear differential equations. This paper is devoted to the investigation of the simplest mathematical models of non-even-aged forests affected by insect pests. Two extremely simple situations are considered: (1) the pest feeds only on young trees; (2) the pest feeds only on old trees. The parameter values of the second model are estimated for the case of balsam fir forests and the eastern spruce budworm. It is shown that an invasion of a small number of pests into a steady-state forest ecosystem could result in intensive oscillations of its age structure. Possible implications of environmental changes in forest ecosystems are also considered.

A simple mathematical model of mono-species forest with two age classes which takes into account seed production and dispersal is presented in the paper. This reaction -diffusion type model is then reduced by means of an asymptotic procedure to a lower dimensional reaction -cross-diffusion model. The existence of standing and travelling wave front solutions corresponding to the forest boundary is shown for the later model. On the basis of the analysis, possible changes in forest boundary dynamics caused by antropogenic impacts are discussed.

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PrefaceThe authors of this paper have made an attempt to make use of mathematical/ statistical techniques to assess the C0 2 data in connection with the results of Global Average models. Ideologically, the time span (of almost 100 years) form the classical works of Arrhenius to the benchmark book "SCOPE 29" is filled by many findings, but even more so by uncertainty. This applies especially to the sphere of prediction -to what degree is it possible to predict the future values of the C0 2 concentration on the basis of the behavior of the past and present values? This paper presents an approach on the basis of the notion of the predictive ability of the model and the functional of the risk of projection. lll BO R. DOGS Leader Environment ProgramTel/us (1991 ) ABSTRACTA new methodological approach for the analysis of monitoring data is discussed. The main ideas are illustrated for the example of the C0 2 problem. The analysis of C0 2 concentrations obtained from a global network of monitoring stations permitted us to construct a nonparametric evaluation of the spatial-temporal distribution of this field. We propose a parabolic parameterization of the long-term tendency of this field as a function of time (in one-year time steps). A function of the predictive ability of a model is defined on the basis of the technique of "supervised training." This function is computed for a parabolic model and it is shown that this model constructed for the first 15 years of observations evaluates the tendency for the next 15 years quite well. The main problem that we solve in this paper is how to correlate the projections of different models for the carbon cycle and different scenarios of the annual release of carbon into the atmosphere with the projections that reflect parameterization of the trends of C0 2 -monitoring data.